6. The relationship with morphological types

In the foregoing sections we have already touched upon the
correlation of a number of physical properties with morphological
type. We will now discuss the available information, in particular
the question whether there is a one-to-one correspondence between
morphological type and one or more physical properties.

We have found that for each galaxy log M(R) is roughly
proportional to
log R, but galaxies with different rotation velocities,
as measured by Vm, have a different constant of
proportionality.
This indicates that the global mass distribution in spiral galaxies
is similar, but galaxies with large Vm are more
densely packed than galaxies with small Vm. The
difference in Hubble type is not evident from the curves of
M(R): for example the Sab galaxy NGC 4151
has about the same M(R) curve as the Sc galaxy
NGC 3198. This seems
to imply that the Hubble type is mainly determined by differences
in the local distribution of matter. It is necessary to assess the
influence of Vm first, before discussing Hubble type
differences. Note that Vm is loosely correlated with
LB and hence connected with
Van den Bergh's luminosity class, but that a precise distinction of
e.g. luminosity class I, I-II and II in terms of different values
for Vm is impossible.

The mass-to-luminosity ratio, both the global one and its radial
distribution, does not correlate well with Hubble type. The ratio
of the surface densities of total mass and HI gas mass in the outer
parts of galaxies correlates better with Vm than with
Hubble type.
There is, however, a striking difference in these ratios in the inner
parts of galaxies of different types. Crudely speaking the ratio of
total mass to HI gas mass in the central regions is decreasing towards
later types. This is the only clear correlation between morphological
type and the physical properties we discussed so far.

Two effects reinforce each other to produce the above correlation: in
early type spirals there is a stronger increase in
M(R) and
a stronger decrease of
HI(R)
towards the centre than in late type
galaxies. Unfortunately, both these quantities cannot be reliably
determined for most of the galaxies in our sample because of beam
smoothing effects (cf. chapter 3 and
6). Although we have corrected
the 21 cm rotation curves in the inner parts of a number of spirals
with optical data we could not do this correction properly for galaxies
with large nuclear bulges. For the influence of beamsmoothing on
the radial distribution of HI gas we cannot correct at all. This
greatly restrains the discussion of the relation between Hubble type
and the gas-to-mass ratio in the central parts. In about 50% of the
number of galaxies in our sample the resolution in the inner parts is
insufficient.

We have investigated whether the shape of the curves of
M(R)
show a relation with morphological type. In general these curves have
a peak in the centre and decrease roughly exponentially outward. The
amplitude of the central peak decreases towards later type, as can be
seen in Fig. 3 of
chapter 6. It is difficult to make this statement
more quantitative. We have tried several ways to do this, but none of
them is very satisfactory. The main difficulty is that we have to
find suitable normalization factors, both for the surface density and
the radial coordinate, otherwise we cannot compare galaxies with
different Vm. We have tried to normalize the
M(R)
curves by scaling
them in the radial direction with the radius at which
M = 50
M
pc-2.
It turns out that there is still a substantial variety in the slope
of the quasi-exponential part of these scaled curves, thus preventing
a consistent procedure to measure the amplitude of the central peak
above the disk. We can, however, make estimates from the fits we made
to the rotation curves with the spheroids and disk models. In
Fig. 13
we show the percentage of mass in the spheroids as function of Hubble
type and Yerkes form. Only a loose correlation exists. We have listed
other quantities, like the ratio of central surface density to central
disk surface density, again determined from the model fits, in
Table 3.

Figure 13. Relative mass in the spheroids
(Msph / Mfit) vs Hubble
type (left) and Yerkes form class (right). Pluses represent
galaxies for which the resolution in the inner parts is poor, dots
represent galaxies for which the resolution in the centre is adequate or
for which a correction has been made with optical data.

We have also-tried to relate the morphological type to the detailed
behaviour of a number of other quantities. Direct comparison of e.g.
rotation curves could be done but many of these are somewhat irregular.
Moreover, the rotation velocity is not a basic physical quantity but
one determined by the distribution of mass and angular momentum. A
convenient way to make comparisons for different galaxies is to study
the behaviour of dimensionless parameters which can be constructed from
the basic physical quantities.

which can be calculated from the curves of the cumulative mass,
M(R), angular momentum, H(R), and kinetic
energy of rotation, E(R).
(R) varies from
0 in the centre to 0.33 ± 0.01 for 22 of the 25
galaxies in our sample. The exceptions are M51 (strange rotation
curve), M33 (the rotation curve we used does not extend beyond a
turnover radius) and M83 (rotation curve comes from one of the
artificial models described by
Hunter and Toomre (1969).
Although we cannot exclude the possibility that the constant value of
(R) is
an artefact of the approximations implicit in the mass model
calculations, the curves of
(R) do
represent a smooth transformation of the
rotation curves. The shape of the
(R) curves is
different for different galaxies: for early type spirals
(R) rises
steeply to about 0.25 and slowly increases over the main disk, and for
late type small galaxies
(R) increases
almost linearly. Late type large galaxies have a curve of
(R)
intermediate between that of early
types and late type small galaxies. In Table 3
we have included a column which gives this information in a quantitative
form: there we present the ratio of radii

A problem with the further interpretation of the
(R)-curves is the
dependence on Ro: if we scale the radial coordinate with
Ro to
achieve a uniform representation we find that e.g. for NGC 2841r = 3.8 if Ro = 7' and
r = 8.7 if Ro = 14'.

This dependence of possible type indicators on Ro is also
present in the other quantities listed in
Table 3. For instance,
in the mass model fits the Toomre disk is fitted first, and for
the nearly flat rotation curves the turnover-radius associated
with this disk had to be taken close to Ro in order to
achieve a
good fit. It is therefore difficult to find a good criterion for
making an ordering of the galaxies in terms of a dynamical sequence.
Nevertheless, there are weak indications that there is not a unique
correspondence of Hubble type or Yerkes form with the dynamical
type indicators we have investigated. From Table 3
we can see that if we use central mass concentration
(logo /
do where
o is the
central surface density and
do
the central surface density of the Toomre disk) as a criterion to form a
dynamical sequence we have in order of
logo /
do :
NGC 4151 (Sab, gk),
NGC 5055 (Sbc, g), M31 (Sb, k), NGC 4736 (Sab, g), NGC 5033 (Sc, g), NGC 2841 (Sb, k),
NGC 4631 (Sd, af), NGC 7331 (Sbc, gk), NGC 4258 (Sbc, g) and so on.
This list contains 5 Hubble stages and 4 Yerkes form classes and
these occur not in their proper sequence. We get more or less the
same list if we use the shape of the
(R)-curve, or
even the quantity Rmax / Ro, where
Rmax is the radius where the
rotation curve becomes roughly flat, as the ordering criterion.

From the above discussion we conclude for the moment that the
morphological stages do not have a one-to-one correspondence with
the physical quantities we can derive from 21 cm line data. Only
the loose correlations, found already in studies of the integral
properties, are found back. In that respect we must emphasize that
correlations derived from integral properties cannot be interpreted
in a straightforward way. For this it is necessary to assume an
"ideal form" of the radial distribution of matter. An interesting
result like the correlation between the shape of the integral HI
profile and Hubble type
(Shostak, 1977)
is not easy to translate
into a statement about the shapes of rotation curves and the forms
of the distribution of
HI in
galaxies of different morphological
types. This can be illustrated by considering Shostak's data for
those galaxies for which a Yerkes form class is available. The
shape of integral HI profiles is usually characterized by two peaks
at either side of the systemic velocity. The peak-to-centre ratio,
p, can be estimated by averaging the amplitude of the two peaks and
dividing it by the amplitude at the systemic velocity (see
Shostak, 1977
for details). In Fig. 14 we show p as function
of Yerkes form
for different Hubble types. p is apparently better correlated with
Hubble type (cf. Shostak's Fig. 1, and the separation of symbols in
Fig. 14) than with Yerkes form, despite the
good correlation between 4
these two classification systems. This result illustrates also that
no simple one-to-one correspondence exists between the morphological
types and physical quantities derived from 21 cm line data.

Figure 14. Peak-to-centre ratio of the HI
profile vs. Yerkes form for the galaxies in the sample of
Shostak (1977).
The various symbols represent different Hubble types.

To conclude, we find that probably only loose correlations can
be found between morphological class and the radial distributions of
total mass and HI gas mass. The luminosity classes are loosely
correlated with the mean rotation velocity Vm. The
Hubble type and
Yerkes form are loosely correlated with the amount of matter in the
central regions in excess to that in the disk. There is a large variety
among galaxies of the same morphological subclass and occasionally
a great similarity between galaxies of different morphological types.
This must be due to differences in the individual history of each
spiral galaxy.